Automorphism groups of nilpotent groups and spaces

Abstract

A pair of finitely generated, torsion-free nilpotent groups G 1, G 2 is constructed with the properties that G 1 and G 2 are p-isomorphic for all primes p, yet Aut( G 1) and Aut( G 2) are not isomorphic. The example constructed is compared to an analogous example in the homotopy category of simply connected, finite CW-complexes.